DKKA'R.'I'IÄHJNT Olf PSIYCHOXJOCJ-Y • UNTVTHlR.emr OF H-IJIITOIS • URBAJMA, HJXJ

METHODS OF ANALYZING GROUP TASKS

GORDON O'BRIEN UNIVERSITY OF ILLINOIS

TECHNICAL REPORT NO. 46 JANUARY, 1967

Communkotion, Cooperation, and N*go>ialion In CulluraMy H*l«rag«n«oui Groupt

Project Supported by the Advanced Research Projects Agency, ARPA Ordjr No. 454

Under Office of Naval Research Contract NR 177-472, Nonr 1834(36)

FRED E. FIEDIE», LAWRENCE M. STOIUSOW, AND HARRY C. TRIANDIS

Principal Investigators

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il mi 0)

D D C

YA MAR 7 1967 | . I i;

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;■?■

GROUP EFflSCTIVENESS RESEARCH LABORATORY

DEPARTMENT OF PSYCHOLOGY

UNIVERSITY OF ILLINOIS

URBANA, ILLINOIS

Methods of Analyzing ""roup Tasks

Gordon O'Brien

University of Illinois

Technical Report No, 46

January 1967

Communication, Cooperation and Negotiation in Culturally Heterogeneous Groups

Project Supported by the

Advanced Research P/ojects Agency, ARPA Order No. 454 Under Office of Naval Research Contract NR 177-472, Nonr 1834(36)

Fred E. Fiedler, Lawrence M. Stolurow, and Harry C. Trlandls Principal Investigators

DISTRIBUTION OF THIS DOCUMENT IS UNLIMITED

Methods of Analyzing Grou; Tasks

Gordon O'Brien

University of Illinois

ABSTRACT

^ In this report, it Is argued that description and classification of

group tasks can best be approached from a theoretical rather than empirical

or factor analytic perspective. It Is pointed out that p«evlous attempts at

task classification generally focus on one of three aspects of the task and

group situation. The literature of group task analysis dealing with each of

these aspects is then reviewed, and It Is pointed out that each bind of task

classification can be comprehended as an attempt to discriminate different

relations existing betv^an various elements of the tapk and group structure.

The contribution of these attempts to a theoretically useful taxonomy of tasks

is evaluated.

Structural role theory Is Introduced as a theoretical framework which

leads to a system for classifying tasks. Digraph theory and matrix algebra

are then applied to the problem of task definition, and indices for the measure-

ment of some Important group task dimensions (Inter-position collaboration,

intor-posltlon co-ordination, inter-task co-ordination, and goal path multipli-

city) are derived. The report concludes with a brief discussion of the prob-

lems and advantages of application of the structural role theory method cf

task analysis. V

Methods of Analyzing Group Tasks

Gordon O'Brl n

University of Illinois

Earlier work by Fiedler (1965) shows that the perform mce of culturally

heterogonoous groups is determined partly by the nature of the group task.

Homocultux>i groups perform better than heterocultural groups only on certain

tasks. This finding suggests that task characteristics deserve closer attention.

It would be desirable to know what kinds of task are likely to produce differen-

ces in performance between houocultural and heterocultural groups. Fiedler has

so far classified tasks along a structural dimension (structured-unstructured).

It is possible that other task dimensions will be important for the understan-

ding of group process (e.g., co-operation requirements, difficulty). This

report will therefore consider some possible ways of classifying tasks and

provide a method of analysis which should be useful In subsequent research on

the determinants of group effectiveness.

I. The Purpose of Task Analysis

The literature of small groups and organization theory, has, during the

last fifteen years, provided a number of reasons for studying group tasks.

This study was partly supported by iMIPA Order 454, Contract Nr 177-472, Nonr-1834(36) with th« Advanced Research Projects Agency and the Office of Naval Research to study "Communication, Cooperation and Negotiation in Cultural- ly Heterogeneous Groups" (F, E. Fiedler, L, M. Stolurow, and H. C, Triandis, principal investigators), "f? remainder of the work was supported by an (Australian) Commonwealth Post-Graduate Award which was held by the author in 1965-1966 at the University of Melbourne, Australia. The author participated In the Structural Role Theory Project (Principal investigator, Oscar A. Oeser) In the Psychology Department at Melbourne University. Consequently, this re- port has benefited considerably from the advice and encouragement of Professor Oeser, Head of the Department of Psychology, Melbourne.

2.

These may be briefly listed:

(I) Taxcmoiuy. In personality analysis, persons are described and com-

pared using a number of general categories and dimensions. The classification

of personality types Is a necessary prerequisite for the precise statement of

hypotheses and generalizations concerning the relation of personality to

specific behaviors. Slnllany, the statement of categories and dimensions of

group tasks should provide a way of identifying different task types and a way

of comparing their differentia.1, effects on group behavior.

(II) Generalization. Studies in social psychology are carried out in

specific situations, whether these be in the laboratory or in natural settings.

Results obtained from these studies are often applied to other situations with-

out a careful examination of the validity of such extrapolation. The appro-

priateness of generalizations should be decided upon after a consideration of

the degree of resemblance between the significant features of the situations

involved. One of the significant features common to all group situations is

the task, and task analysis would therefore help social psychologists to evalu-

ate the generalization range of their findings. Findings derived from studies

in the laboratory, for example, may not be directly applicable to actual or-

ganizations because there are marked differences in the tasks which are per-

formed in the two settings (Golemblewski, 1962; Welck, 1965).

^ili^ Theoretical integrt-tion. If the task of a group is to be treated

seriously, and not Just dismissed as a difficult si^uational variable which

needs to be controlled, then a way of relating task characteristics to other

elements of group structure is needed. Task analysis would provide a means

of meeting this need. Many writers have emphasized the importance of task

analysis for theoretical integration in social psychology (e.g.. Carter et al.,

1950; Roseborough, 1953; Roby &■ Lanzetta, 1958; Hare, 1962; Shaw, 1963; Oeser &

Harary, 1962, 1964; Anderson & Fiedler, 1964; HcGrath, 196S; McGrath & Altaian,

1966).

3.

(iv) Description. Inclusion of task analysis In a conceptual scheme should

help to Interpret and explain a vvlder range of findings. It should als" lead

to finer description of group behavior. Different activities may be associated

with different aspects of group structure. Where task is treated as a major

element of group structure, then observation of group activities will distin-

guish activities largely associated with task performance from activities which

constitute interpersonal behavior. Thus, Baj.es (1950) distinguishes task

functions from socio-emotional functions in his method of process analysis.

Task activities are also deliberately separated from "personal" activities in

the research of Herbst (1952, 1953); Wilson, Trist & Curie (1952); Rice (1958);

and Trist et al., (1963). This separation forms the basis for a comprehensive

behavior description which, in turn, is the foundation of a theoretical struc-

ture which relates task analysis to social behavior.

II, Possible Types of Task Analysis

Analysis of group tasks involves an examination of :he ways in which the

task can be related to other features of the group structure. In some ways,

this analysis is similar to the method of describing the meaning of a theoreti-

cal term. The main similarity stems from the "relational" quality of tasks and

theoretical terms. A theoretical construct is related to other theoretical

constructs, logical terms, and data terms by a set of syntactic and logical

rules. Specification of these rules describes the actual and possible ways in

which the construct is connected to other elements of the theoretical system.

In this way, the meaning of the construct is demonstrated. Similarly, the

analysis of a task is given by describing the permissible relationships between

2 it and other elements of group structure.

2 It is possible to analyze tasks In a purely empirical or atheototical

manner. For example, Hech^an (1966) and Morris (1965) classified tasks in terms

4.

Considered in this way, task analysis is inevitably associated with a

set of concepts of group structure and relationships. Whatever set of con-

cepts is used to describe groups, reference is made to two aspects of groups

(other than tasks). These aspects are associated with persons who are mem-

bers of the group, and an organization which structures the relationships be-

tween persons. Using these general and rather vague notions of orsons and

organization, types of task analyses may be described.

(a) Task-task analysis. HCi-e the task is considered in relation to itself.

The task is considered as a system with component parts and relations, and par-

ticular tasks are described in terms of a particular "configuratlou" in the

component parts,

(b) Task-organization analysis. In this kind of analysis, a particular

task is described through examination of the relationships holdinc between the

task system and the organizational structure.

(c) Task-person analysis. The final kind of task description is achieved

when characteristics, abilities, and states of persons are related to specific

characteristics of the task»

At present, these types of analyses will not be examined in detail. This

of qualitative descriptions of the task Instructions ("produce" or "discuss" or "solve"). These descriptions did not state any relationship to group struc- ture and this was done deliberately, for they tried to determine the consequen- ces for group structure and behavior of the task types. Their work must there- fore be viewed as a prelude to task analysis. The approach of Altman (1966a, 1966b) is also an empirical one, although he does use an arbitrary classifica- tion scheme for describing task behavior. Altman maintains that the analysis of group tasks should be based on a classification of the group behaviors whi:h they produce. Hence, the complete analysis of group behavior must await the result of systematic studies of the relationship between tasks and group be- havior. The importance of relating task analysis to behavior cannot be disputed, but it appears that this can be best done when there is available a way of describing tasks independently of group behavior.

Wf

s.

will be done in the course of a review of current methods of analyzing tasks.

They are mentioned at this point because they serve, firstly, to Illustrate

what is meant by the "relational" quality of task analysis, and secondly,

because the three type» help to classify existing methods of analysis. The

following brief review of methods of group task analysis will reveal that

most Methods can be classified as belonging to one or another of the three

types above.

III. Review of the Literature on Group Tark Anaxysis

This review has two alms. The first aim is to organize existing methods

of analyzing group tasks. The second aim is to evaluate the contribution of

the various types of analysis to the construction of a general taxonomy of

tasks which is, at the same time, theoretically useful. It is realized that

most of the schemes and classifications to be considered were constructed for

immediate and specific purposes. So, in some ways, any criticisms of these

approaches will be unfair, Lafitte is correct when he states that "any scheme

of Job description, analysis or classification is as good as any other so long

as it serves its purpose" (Lafitte, 1958, p. 66). However, it is still

reasonable to see if purposes other than those intended are also achieved.

Any criticism made then, in the course of this review, does not imply that the

relevant analysis is unsatiffactory when Judged against its own aims.

Task-Task Analysis

Because of the "individual" orientation of social psychology, there are

few accounts which treat tasks independently of persons and group organization.

Task-task analysis is characterized by a concern with the division into sub-

tasks and the relationships which order the sub-tasks. In the study of flow

charts, or work study, the group's (or organization's) goal is broken up into

a set of sub-tasks or "operations" which are ordered by temporal relationships

0.

with various sodalities,, The temporal relationships indicate the order of

precedence for the sub-tasks while the modality refers to whether a sub-task

"may' nr "must" occur after a certain sub-task. In critical path analysis

(Shaffer, Ritter ft Meyer, 1965), the group task is split up into sub-tasks

which are then given an estimated completion time. The sub-tasks arc then con-

nected by lines which represent precedence relationships on the sub-tasks.

After these relationships have been specified, a "critical path" Joining the

sub-tasks is ^aJculated. This path shows the most efficient way in which the

total task can be completed« Work engineers are Interested in this method of

task analysis because efficiency is increased and costs lowered. Occasionally

this kind of task analysis in a. simple form is used by psychologists. For

example. Guest (1962) observed that poor productivity and negative social

relationships In an automobile factory were pa.-tly due to inappropz l^te sub-

task engineering on tlie assembly line. Another example is given by Katz and

Kahn (I960). In considering what leadership style was effective for supervisors,

they used an analysis of the work group task which described it in terms of

two sub-tasks planning and actual operation on materials. Both of thase

examples refer to Instances where the investigator used a simple type of task-

task analysis for the purpose of understanding social behavior in a specific

situation. Analyses which are general in their application are much rarer

in occurrence. One example of a general approach is Roby's treatment of sub-

task phasing in small groups (1962), Roby was concerned with the problem of

defining and ordering task segments and the consequences of particular task

phasing for gro ip behavior.

Task-Organization Analysis

The second kind of group task analysis is largely concerned with describing

how tasks may require the group to organize its activities in various ways.

7.

Within this class of analysis, two major types may b« discerned. The first

type is based on a mechanical input-output model, while the second type des-

cribes the task in terms of co-operation requirements. The input-output analy-

sis will be considered first,

(1) Group task analysis in terms of input-output variables. Several

studies by Lanzetta and Roby on group task performance were followed by a

theoretical paper on the analysis of group tasks (Roby & Lanzetta, 1958). In

this paper, they proposed a method of describing "group-task" charajteristics.

Essentially, each task provided an "input" to a group which had to be dealt

with in a certain way If a specified state of the physical environment was to

be changed or maintained. The performance of the task could be described using

four different sets of "events" (task input, group input, group output, task

output). This description of the group-task system is depicted schematically

in Figure 1 (after Roby & Lanzetta, 1958).

Event Sets

T, G G T T. ; feedback) 1 1 o o 1

Figure 1.

Roby & Lanzetta*s paradigm for the description of group tasks

The set of events (t.,, t _....) occurs in the general surroundings of

the group and the entire class of such events is denoted by T ("the class of

task input variables"). Examples of the events given Include variation in

8.

"input displays," and stress-inducing stimuli. G designates the class of

group icmit activities which occurs within the group as a corsequence of T .

Examples include attending or observational responses. Following the occurrence

of activities In G., thero occurs group output activities (G ), These re- 1 • Q

sponses lead ti . further class of events (t ,, t ..,.,) in the external environ- Ol 02

uient. These events constitute the class of task output variables T , Some sub- o

set of events in T generally forms the basis for evaluation of group perform-

ance.

Roby and Lanzetta link the group input and output events to certain posi-

tions in the group. Complete task description then involves the specification

of the appropriate task events T , together with the distribution of G and

G activities which are associated with the various group positions. This task

analysis then Involves the description of the "physical*' properties of the task,

specification of the grcp "activities" required, and listing of the ways in

which these activities are allocated. At a later stage of their article, they

consider that tasks can be further described in terms of more abstract organi-

zational requirements. Thuse requirements are called "critical demands" and

are of three types. The first demand is orientation which denotes the function

of determining the condition of variables in t e task environment. The second

demand is mapping, "the process by which a group anticipates or learns the

consequences of various action alternatives mrfer various environmental con-

ditions" (Roby & Lanzetta, 19S8, p. 96). The final demand is jurisdiction,

and this refers to the pr icesses whereby response actions are chosen and de-

cif4ons implemented.

This analysis stresses the close relationship vvnich exists between a

group task, group organization, and individual activities. Furthermore, it

maintains that group tasks may be characterized by the group processes which

"•"«,

9.

they Induce (or "demand"). Its usefulness as a method of task analysis, how-

ever, appears limited because (a) of the lack of clarity in key terms like

"event" and "action," (b) the "input-output" dichotomy does not provide a means

of analyzing the sets of behaviors that intervene between the reception of

..nformation nd the final goal achievement activities (for instance, how are

i

those activities understandable in terms of structural dimensions such as

power and communication?), (c) no information is given about the dimensions

used for describing task variablesf (d) the analysis seems to be applicable to

only a limited number of tasks. These are tasks which require individuals to

deal with changing sources of "information" «cording to a c.learxy defined set

of observations and procedures.

Another analysis which classifies tasks In terms of their requirement for

organization is that of Christie (1956). The task is viewed us a problem in

information handling; as an input an-i output to the group, it is described by

its content, form, time, and locus. The task is aleo defined by the operational

modes imposed on the group, and by the organisations developed by the group.

Like the analyses of Roby and Lanzetta, group organization is evaluated

through assessing Its information handling characteristics. This approach

tends to neglect the systematic study of the organization as a determinant

• t task performance. Either tie organizational & Picture is defined by its

Information processing fuactlons without description of the organizational

ptructure as a system independent of task, or else only one type of organiza-

tional structure is treated. This latter procedure is adopted by Christie who

concentrates on the communication structure. Another similarity of the Christie

analysis to that of Roby and Lanzetta is in the small range of tasks to which

it can be applied. Tasks Involving the synthesis of elements of verbal or

written information are the concern of Christie's analysis, and it has been

applied only to the kind of task traditionally used in the communication network

10.

studies (Bavelas, 1950; Leavltt, 1951; Shaw, 1964).

(11) Group task analysis and co-operation requirements. A number of

writers have described tasks by examining the tyv of allocation required for

task performance (Lewis, 1944; Thomas, 1957; Kelly & Thlbaut, 1959; Fiedler,

1964; McGrath, 1965; Welck, 1965).

(a) Cumulative Interdependenae. This kind of interdependence occurs when

the product which one person produces becomes the input for another person.

Assembly line tasks typically have high cumulative interdependence. The stan-

dar.1 of task performance of any person is limited by the quality of tL? input

which he receives. Group tasks of this type are described by Lewka (1944)

using the terms "specialization of labor/' while Thomas (1957) refers to this

type of Interdependence in terms of high "facilitation In means control."

(b) Disjunctive interdependence. Disjunction exists when group task

accomplishment depends on one person in the group performing the appropriate

task. Once this task Is complated by one person, »he group task is also com-

pleted (Thlbaut b Kelly, 1959, p. 62). The appropriate action does not neces-

sarily depend on any prior sub-task performance. A disjunctive task requires

minimal interdependence. Because only one person needs to produce the solu-

tion, "a disjunctive task permits group members to work independencly without

communication or coordination of their efforts" (Thlbaut & Kelly, 195&, p. 163)

Examples of disjunctive taeks would be presented where there are group

tasks requiring one "correct" solution, e.g., in logical or planning, tasks.

A group ol advertising executives convened to croons a new slogan for a pic-

duct, has high disjunctive Interdependence.

(c) Conjunctive Interdependence. With a conjunctive group task, all mem-

bers have to make a specific response If the group is to succeed (Thlbaut &

Kelly, 1959, p. 162). With this type of task, each person must complete his

sub-task, or else the group is unproductive. When a group is required to

11.

achieve consensus in its opinions or attitudes, then conjunctive interdepen-

dence is high.

Analysis of tasks using the idea of interdependence focuses on the way

ir which sub-tasks are distributed amongst persons or positions in a group.

This kind of task analysis is especially promising for the study of interper-

sonal relationships in work groups. Hie types of informal relationships (e.g.,

affective, communicative) which are found may be easily related to the kind

of group task and its associated type of interdependence. There are a number

of difficulties in this type ol analysis, how.ver, which need to be met before

it can be rigorously applied to the study of group performance. One difficulty

derives from the fact that group tasks often require various combinations of

interdependence. Another difficulty is due to the classlficatory nature of

this analysis. Eventually,, the analysis should provide a way of measuring the

amount of a given kind of interdependence present in a particular group task.

At present, group tasks are merely assigned to one or another of the specified

categories.

Task-Person Analysis

A group task mav be related to persons in a number of ways. Firstly, a

group task may require that group members possess certain skills or abilities.

Secondly, the group task may determine to. a large extent the number and kinds

of activities in which a person engages. Thirdly, a group task may affect the

opinions and attitudes of persons. These attitudes may be related directly

to the task or to other persons involved in the task situation.

Analysis of tasks which concentrate on the task-person relationships are

found mainly in the writings of industrial psychologists who have been preoccu-

pied with the problem of fitting a person, or a group of persons, tc the work

task. A common approach is known as -<ob analysis where the activities of

12.

workers ere studied without direct reference to the Job or product Involved

(Palmer £. McCärmick, 1961), McCorralck's work involved appli-

cation of factor analysis to description of worker activities associated with

various Jobs. His results suggested that the variety of human work activities

could be identified or measured using a relatively small number of independent

dia«nsions.

The description of "activities" is a first step to the specification of

skills required for a group task. If a group task requires some people to

perform arithmetical operations, then son» persons assigned to the group should

be skilled in arithmetic. Thus, tasks have also been analyzed by listing the

skills required in the persons assigned. Personnel managers and vocational

guidance officers have their particular "job requirements" lists, but more

general classificatory systems have been developed which attempt to organize

Job requirements using a limited number of independent dimensions (Coombs &

Satter, 1949; UcCormick, Finn, & Scheips, 1957).

This way of describing tasks complements the previous task descriptions

through its emphasis on the effect of personal characteristics on task perform-

ance. Task performance is influenced not only by the formal task structure

and the group organization associated with this task organization« It is also

affected by the distribution of personal characteristics and skills required

for its completion. It may also be characterized by the degree to which the

skills required by the task are matched t the abilities of the group members.

One way of describing this matching is by saying that the task is more or less

difficult. Difficulty level has been used by »lorrissette, Pearson, and Switzer

(19415) to define task types. They defined difficulty levels using a mathematical

formula for entropy. In information theory, entropy defines the degree of

randomness of events emitted by an information source. Entropy values ob Lsed

using information theory definitions were taken as measures of task difficulty.

——V» -^

13.

By using a particular task In various communication nets, Morrlssett" et al.

fonnd that their definition of task difficulty corresponded closely to task

difficulty as qualitatively defined. This analysis of tatk properties should

make possibly a more precise study of the interactive effects of task difficul-

ty, task load, and communication structure upon group performance. Iv.s range

of application, however, appears to be limited to communication network studies.

The analysis deals with but two dimensions, difficulty and task load, and is

appropriate only for tasks which have an objective solution attained through

the exchange of "information" among all members of a group.

A final way of describing tasks throvvh their relationship to persons,

focuses not on personal skills and activities, but on internal states and needs.

A task may facilitate or hinder a person in his attempt to satisfy or express

certain needs. These methods of task analysis have been employed by workers

of Tavlstock Institute in their discussion of "soclo-technlcal" systems

(Trist & Bamforth, 1951; Rice, 1958, 1963; Emery & Trist, 1960). These

sriters describe task organization not only in relation to productivitv, but

also in terms of its effect on personal satisfactions. Thus, Rice (1958, ch. 4)

characterizes primary work tasks by assessing the extent to which (a) the task

allows those engaged on it to experience the completion of the "whole" task,

(b) the task allows those engaged on it to control their own activities, and

(c) the task allows workers to form satisfactory personal relationships.

A number of other writers, working independently, have also defined tasks

in relation to personal satisfaction, and they provide further evidence ?or

believing that the criteria listed by Rice not only differentiate tasks, but

they are also the criteria which the worker himself associates with Job satis-

faction. Lafitt" Interviewed, from different factories, a large number of

workers who performed a r&nge of Jobs (Lafitte, 1958, ch. 4). Results showed

14.

that Job satisfaction was significantly relatad to the worker-defined dimensions

of cleanness, completeness (Rice's criterion (a) ), and independence (criterion

(b) ). Using these criteria, Lafltte was able to construct a classification

of Jobs. Oaaling with a narrower range of factory Jobs those Involving

repetitive operations—•Baldamus noted that workers gained satisfaction due to

a task property which he temed "traction" (Baldamus, 1931, ch. 4). Different

kinds of traction were postulated, but the ideas of "independence" and "com-

pleteness" were closely associated with all forms.

Tasks have been related to personal satisfaction in the laboratory setting

also. The significance of task "completeness" for personal satisfaction has

been studied in the course of research into the Zelgarnik effect, while the

"control" dimension of tasks has been related to task performance by Trow (1957),

using a concept of "autonomy," and by Mulder (1959) who used a similar concept—

"self-realization."

Hie description of tasks in terms of their consequences for personal

satisfaction has been used successfully in the development of productive work

groups, but so far the task description is linked too closely with the speci-

fic situations which were studied. A general, abstract account would take

the analysis further by identifying what objective characteristics of tasks

f related to personal needs. Also, in many instances, it is not clear

whether "the task" refers to the organization of the sub-tasks, or the cross-

organization between the sub-task pattern and other properties of the group,

like power and communications structures.

Another diffic ;y concerns the application of this task analysis to

group tasks. It is fairly clear that sub-tasks can be classified by reference

to general needs and worker satisfaction. But a group task is composed of a

set of sub-tasks. If each sub-task is classified differently, using this

task-person analysis, how is the group task, considered as a set of sub-tasks.

15.

to be classified?

If a group task ha^ four sub-tasks and two of them allow a worker a large

amount of control, whereas the other two give the worker little control, then

the group task might be classified as one which gives group members a medium

amount of control over their own activities. This single measure would obscure,

however, the differences among sub-tasks. It Is probable that knowledge of

such differences In sub-tasks would be more useful In explaining task perform-

ance than a holistic rating of the group task.

Scale Analysis of Group Tasks

A method of task analysis which is not easily fitted into the previous

classification is scale analysis. Shaw (1963) used a technique for scaling

group tasks which is similar to that used by Thurstone and Chave (1929) for

attitude scaling. Ten dimensions of group tasks were postulated and 104 tasks

were scaled on eacfc dimension. After two successive factor analyses and on

certain theoretical grounds, six task dimensions were retained. They were

defined as follows:

A. Difficulty — the amount of effort required to complete the task.

B. Solution Multiplicity — the number of possible solutions deemed to

be correct. This dimension also included the number of alternatives

for task completion (goal path multiplicity) and the degree to which

accpetable solutions can be verified (i.e., deaonstrated co be correct).

C. Co-operation Requirements — a measure of the degree to which inte-

grated action of group members is required to complete the task.

Shaw found chat dimensions A, B, and C were the most stable. Other dimen-

sions were:

0. Intellectual Manipulative Reaulrements — the ratio of mental tc

motor requirements.

16.

E. Population Familiarity — the extent to which the task is encountered

by members of the "larger" society.

F. Intrinsic Interest — the degree to which the task in and of Itself

Is Interesting, motivating, or attractive to the group members.

Four of Shaw's original ten dlmanslons (decision veriflabllity, goal

path multiplicity, solution specificity, goal clarity) were used by Fiedler

(1963, 1905) to define the degree to which a group task is structured (its de-

gree of clarity or ambiguity). Shaw's task dimensions differ In type. Dimen-

sion B (solution multiplicity) Is defined by the formal or objective structure

of the task. Other dimensions (A, D, E) are defined by the skills and know-

ledge required by the group members, if the task is to be completed. Dimension

C is defined by aspects of group organisation required if the ta&x Is to be

completed, while Dimension F is defined by one of many possible attitudes to

the task.

Scale analysis has resulted in the specification of task dimensions which

refer to a number of diffeent ways in which the task can be related to group

organization and member characteristics. These dimensions are stated very

broadly, and it seems that further development should be in the direction of

establishing a set of concepts, this set allowing the relationships between task

and group structure to be more finely described.

This review of the literature on group task analysis has shown that the

task can be defined by a set of relationships connecting the task structure

to other elements of the group. For the purposes of a comprehensive analysis

of tasks, most of the classifications referred to deal with a limited number

of relationships. This deficiency is only partly explained by reference to

the practical or more limited concerns of the authors. It is also explained

to some oxtent by the absence of a conceptual scheme which defines the major

elements and relationships of group structure. If such a schemo were available,

17.

then a task analysis couJd be constructed which was both comprehensive and

precise. Also, content and precision could be given tc the "field" or "system"

character of group ncructure. The value of a precise method of group des-

cription for the developmen. of a comprehensive task analysis will be shown

in the next section,

IV. Task Analysis in Structural Role Theory

Having discussed the significance of the task system for the theory of

group structure, and reviewed some of the Inadequacies of the literature, we

shall now use structural role theory to outline a system for classifying tasks

and defining some of their properties.

A structural role analysis of tasks endeavors to define a task in terms

of the totality of relations Included in a structural role digraph. The two

et rller papers on structural role theory (Oeser & Harary, 1962, 1964) defined

"group structure" in terms of three elements and five types of relations. Hie

3 three elements defined are:

task — a primitive term meaning anything that has to be done (which thus

can IncluJe "mental" tasks);

person — defiued as a human being who has no relationships to other

human beings except for those laid down by the rules of his

office, and no characteristics other than those prescribed for

assigning him to the occupancy of a given position;

position — defined as a location on an organization chart, a concept

3 The three elements defined correspond to the three dimensions of the

group-task situation which are used by Fiedler (1964). These dimensions are task structure, leader acceptance (Interpersonal) and position power.

18.

which gains Its meaning through being connected (a) to oersons

by assignment relations, (b) to tasks by the allocation rela-

tion, and (c) to other positions by the power relation.

The terminology of digraph theory was used to Illustrate ari describe how

any given sets of these three elements may be logically interrelated« The

terminology used in structural role theory is summarized schematically in Figure

2 (after Oeser & Harary, 1962).

This postulated set of elements and relations is used TO create "ideal

4 tyne" group structure , similar in kind to the institution "ideal types" des-

cribed by Max Weber (1949). Ideal types, when given empirical interpretation

through a set of co-ordinating definitions, are powerful devices for the com-

paratlve analysis of group structures and processes.

H-graph

H-P-graph

P-graph

P-T-graph

t-graph

Relations

Figure 2.

the schematic digraph, 0, of a Structural Role System (after Oeser & Hararj, 1962)

Ideal types, like mathematical models, are used to represent, at an ab- stract level, the underlying logical structure contained in a set of descriptive statements. The postulated eet of elements and relations provides the abstract categories to be used in constructing spoclfic, yet abstract ideal types. Ideal types are created for "real" kinds of groups (e.g.( "bureaucratic" groups, fac- tory groteps, school groups) when a particular ordering of elements by the rela- tions is used. Ideal types are unlike mathematical models in that they are gen- erally constructed from observations of empirical reality. Objects and relation- ships are abstracted from concrete events in order to provide a logically con- sistent, "idealized" description of that type of event.

See Bendlx (1962), and Uartingdsle (1959).

19.

Terminology for Figure 2

D s the digraph of the role system

H « h,«...h m the set of persons i n

P * p.....p = the set of positions i n

T = t.,.,,t » the s >t of tasks i n

R0 * R00* R01***,R0 " the set 0' in'ormal social relations

R » the power relation

R_ = the task precedence relation

R at the person assignment relation

R. » the task allocation relation 4

R- m the induced relation, persons to fasks

For the axiomatic definition of these relations, see Oeser and Harary (1904).

In structural role theory, the analysis of group tasks is carried out by

considering the possible ways in which tM group goal can be related to the

total set of elements and relations. Hence, the major advantages of this

conceptualization are firstly, its ability to relate a pert of the group struc-

ture (the task system) to the total structure. Content and precision oan thus

be given to the "field" or "system" character of group structure. Secondly,

because a formally adequate definition of structure is given, it is logically

possibla to describe group processes over time in terms of the sets of relations

on the elements. Thirdly, specifying the set of relations enaMes a classifi-

cation to be made of the type of relations connecting the tasks.

In any task analysis it is necessary to distinguish between five aspects:

(I) The formal analysis of the task; this consists intially of specifying

the number of sub-tasks and the set of precedence relationships (Oeser &

Harary, 1962, 1964) which may be used to order the sub-tasks. (R»).

(II) The group organization required by the task; this requires specifi-

cation of what task elements are allocated to what positions (R.), and 4

zu.

the typjs of power structures (R ) required for task completion.

'11) The skills and knowledge required to do the task. (R„).

The attitudes which the Individual members may have to the task. (R_) 9

(v) The individual's perception or "image" of the task, which may differ

markedly from the actual task, or from how the individual's super- or

subordinates perceive it.

The rest of this report will consider some of the possible task relations

and outline some formal operations which provide a basis for the comparative

analyses of group tasks«

g ' • 52 PorsoP'Task Relations

Suppose two persons, h and b , have been assigned to three positions,

p., p2, p., and five tasks have been allocates to these positions in the manner

shown in Figure 3.

Figure 3.

Digraph of a Role System

Let numerical weights be given to the relationships in R (the rules of

assignment) end R. (the rules of task allocation). The weights must be ex-

pressed so that the following conditions are met:

a+b»l, cal, D+e+fsl, 0+h«l, 1 + J « 1.

6 Thu content of this action Is derived from a Joint paper by Oeser and

O'Bilep in Human Relations, (in press).

••->r_

21.

The relations R« and R may now be represented In matrix form. The

matrix 1L representing the R3 relation *s:

M.

pi

b

o

while the corresponding matrix M for R. Is:

"a "

M4 =

d

o

o

e

o

o

f

g

o

o

h

1

V

Their product M = M • M gives an Induced relation R. with domain H and

range T. Oeser and Harary (1964, p. llf) illustrated the usefulness of this

operation for obtaining the induced relation of time distribution of people

directly to tasks (by eliminating positions).

This kind of analysis can be used for other purposes« It is possible to

specify attitudlnal relations between persons and tayks. Consider the relation

of ''valuing." This le an "informal" relation which is established when an Indi-

vidual starts working at a task. Assume that h has n tasks and that the

measures of the Intensities of valuing are v., v..*.,,, v . Th?se measures 1 £ n

can be transformed so that n, , . Similarly, for the n„ tasks of h„, etc. a «1 2 2*

fl

The adjacency matrix of valuing, M , can now be written out for persons-

tasks and this can be directly compared with the induced matrix BL. Recall

that M_ defines the apportioning of time by each person h. to each task element 5 1

22.

t ag computed from the explicit structural rules of the organization. M de-

fines the apportioning of "valuing" as experienced by each h for each t ,

Consider the numerical examples of two matrices M and M (the M matrix 5 V O

ie taken from p. 14 of Oeser and Harary (1964) ).

W

1

2

1

50

L o

20

0

i

2

50

40

80

40

3

0

42

0

10

r4

0

16

0

40

5

0

"1 0

10

Both matrices, M_ and H , are ways of reprerenting the person-task-rela- o v

tlonships within a group. The first relation, M , is formal, the second In-

formal. The properties of these relations can be investigated through further

operations on the matrices; and each relationship in M_ can be compared with 5

each relationship in M . (For example, one uight enqulve what consequences

follow from the fact that although t and t have "time-weights" of 50, 50 for

person h , ne nonetheless gives them "va^ue-welghts" 20, 80).

In the saae way, each person can rate his liking for his various positions.

If he has one position only, the measure of his liking (at the first level of

psychological analysis) will perforce be 1.0. If he has two positions, he may

apportion his liking in the ratio o.6 to 0.4 and so on. Whatever rating measures

are used, they can be transformed so that their sum is equal to 1.0. The ad-

jacency matrix of "valuing" can bo written for person-positions. This can be

compared with the adjacency matrix of positions-^asks, in which positions are

asjlgned "weights" by the rules of the organization. Tht.t is, the rules lay

down what proportion of time is to be spent on each of the task elements alloca-

ted to a given position, and theae proportions indicate the "weight" or

23.

"importance" of each tzak element* It seems reasonable to assume that dis-

crepancies and fluctuations in productivity will be connected with discrepancies

In the "valuing" weights attributed by persons to their positions and their

tasks, and the task "weights" attributed to tasks by the rules of the organiza-

tion.

2. Position-Task Relations

The task allocation relation. R.. orders the set of positions and tasks. 4

Part of the formal role of a porltlon Is given by specifying what tasks are

connected to the position. The formal role of position p is defined by the

digraph which contains p and all elements of the H, P, and T graphs adjacent

with p.

In Figure 4, the formal role of position p consists of

(I) the assignment relationship (h , p )

1 (II) the set of power relationships ) (P,» P«^ (Pj» Po)/

(ill) the set of task allocation relationships (p , t ), (p , t )

In an actual group, wivh a fixed number of positions and a x'ixed number of tasks,

the allocation of tasks to positions may vary considerably. Consider a simple

structure with two positions (p , p0) and two tasks (t,, t ).

Figure 5 shows the posiible methods of allocating tasks to positions so

that at least one task is allocated to each position.

Figure 4.

Relationships on position p

24.

(1) (3)

(8) (4)

Figure 5.

P-T Digraph

Inspection of these diagrams at once suggests a more precisa «ay of

specifying what is meant by "degree of co-operation." Instead of the word

"co-operation" we shall use "collaboration," which is a neutral term.

If a Joint allocation of a task to a position is made, this requires that

h and h , In position p. and p-, must collaborate . Therefore, one can inves- X i i. £

ttgate:

(a) the degree of collaboration between p , p. demanded by the structural

role system

(b) tne degree of actual or fancied collaboration.

Clearly, some situations demand more collaboration than others. Thus, in

Figure 5, situation 4 requires more collaboration than situation 3, which in

turn requires more collaboration than situation 1, They differ on a dimension

of inter-position collaboration (as distinct from inter-task co-ordination which

will be discussed later).

For ordering groups on the degree of inter-position collaboration (C ), pt

it is desirable to have a formula which gives zero value to situations like

sltuationl, where there is no sharing of tasks at all, and a maximum value of

25.

1 to situations where all positions share all tasks.

7 A formula which satisfleD this requirement is

n

jfi ld(V-n

V n (m - 1)

where ld(t ) = the in-degree of points t ,

i.e., the number of lines to t from

the P-graph

n = number of tasks

m a number of positions.

The values for C for the situations in Figure 5 are

Situation C . _pt

1 0.0

2 0.5

3 0.5

4 1.0

Sometimes tasks require inter-position co-ordination together with, or

instead of inter-position collaboration. Co-ordination between positions is

required because the sub-tasks are ordered by precedence relationship. Consider

a group with two positions (p , p.) and four sub-tasks (t , t-, t , t ). Some

of the ways in which the positions may be allocated to the sub-tasks are shown

in Figure 6.

For a given T graph, Figure 6 shows that the degree of "mesh" of the task

systems of p and p may vary considerably. In (1) and (3), these systems are

7 I would like to acknowledge the assistance of S. Pelczynski in the

derivation of this formula.

26.

(2)

(3) (4)

Figure 6.

Combined P-T, and T Digraph

temporally separated, but in (2) and (4) co-ordination Is required if the total

task Is to be completed.

The amount of inter-positIon co-ordination not only depends, however, on

the particular allocation of tanks to positions. It also depends upon the T

graph. Figure 7 depicts digraphs showing some of the ways in which the T graph

may produce different kinds of irter-position co-ordination.

A quantitative index of inter-position co-ordination can be derived using

matrices . Let |_TTj be the adjacency matrix for the task precedence digraph.

In this matrix, the rows and columns correspond to sub-tasks and the entry

8.

«e H.^^^r"n:„rcart.rX"96n^br«.,,lgraph8 ^ ^ "^^

27.

(5) (6)

(7)

Figure 7.

Combined T and P-T Digraphs

Vj * 1 lf line titj iB'ln ^e T graph, while t^ = 0 if line tt is not

in the T graph. Let [PTJ be the task allocation matrix where entry p t « 1 if

sub-task tj is allocated to p1 and entry p^ - 0 if sub-task ^ Is not allocated

to pi.

Let 'rr]1 be the transpose of this matrix. This is obtained from [PT] by

28.

Interchanging its rows and columns. Thus, the 1, j entry of I PTj is the same

as the j, 1 entry of I PTj .

Consider the digraph (1) in Figure 6 (reproduced as Figure 8).

Pr

tt~+-~t2 ^ t3Z "%

Figure 8.

Combined T and P-T Digraph

For this digraph, the corresponding matrices are

[TT]«

0

0

0

0

1

0

0

0

0

1

0

0

V 0

0

1

0

[PT]

H1

1

1

0

0

0

1

Using matrix multiplication, the matrix [PT]* is obtained.

[PTj* =[PTJ«LTTJ

The

0

0

1

0 0

V 0

1

[_PTjmatrix gives for any p the number of paths of length 2 connecting p to

p . The number of paths of length 2 from p to t in the digraph is 1, and this

29.

is shown In entry P,^ of the PTI matrix. The number of paths of length

n from p to t is given by entry p t in the matrix formed fromlPTj«[TTJ"* . i J i j

The matrix [PP j is obtained by multiplying [PTJ by [PT} .

[pp] » [PT]* • [PT]1 1 1

0 1

The entry p p of this matrix gives the number of tiaas a sub-task allocated to

p must follow consecutively a sub -task allocated to p .

In Figure 8, p "changes over" to p,. on the completion of t . Also, p X it A \

changes to p. on the completion of t . As shown, in |_PpJ , entries PjP«» and

P1P1-

The matrices associated with digraphs (2) - (8) are listed below. The

interpretation holds for all cases.

(2) jppi M: :I C3)

(4)

(6)

C8)

[icj

2 1 0 0

1 1 1 0

0 2 0 1

(5)

(7)

0 2 0 1

0 2 0 1

An index of inter-position co-ordination will increase as the number of

changes" from p to p Increases. Also, for a fixed number of such changes,

the index should be greater where the number of positions is less. An invertse

index that seems to Jit their requirements well is

CO pt

Sum of entries in main diagonal Sum of all entries

I.e., CO Pt

E diagonal Z total

30.

The values for Cc for the situations In Figure 6 are

Situation CO , pt

1 0,67

2 0.00

3 0.67

4 0.33

This means that Inter-position co-ordination is greatest for situation 2 and

least for 1 and 3, with 4 intermediate.

A big advantage of an index such as CO ^ Is that it can be calculated p«.

from quite complicated digraphs. CO for a complicated task will be calculated pt

thus. Suppose that a given group task cap be divided into two sets of tasks

such that any task of the second set can only bo completed if one or more tasks

of the first set are completed. This type of situation could occur when the

first set of tasks required observations of pointer reading, e.g., in an air-

plane cockpit, and the second set of tasks involved instrument adjustments. An

Instrument adjustment could only be made if, say, two pointer observations had

been made. Let the total number of tasks be 12, and the number of positions be

3. A possible T graph is shewn in Figure 9.

Figure 9.

T graph

A possible P graph is shown In Figure 10.

31.

s

8 "10

Figure 10.

P-T digraph

For this situation w 2 2 0

12 1

10 3

and CO x x 7/12 » 0.58. pt

Other indices could be constructed from the PP matrix. Thus, '* task

load index could be given by the total sum of all entries.

3, Task-lrask-Relat ions

The relationships between the tasks of a group may be depicted in a T

graph, the points of which are tasks and the directed lines of which stand

for precedence relationships the order In which the tasks are to be done.

For example, Figure 11 represents a possible T graph.

t:

Figure 11,

T graph

Hie Job has a beginning (t ) and an end (ta), and the completion of the

whole task system is the goal of the group. It is possible to reach tfl and

attain the goal by three alternate complete paths. Iheae are t., t., t • 16 8

32.

t lf t2' S' t4' t5, ^^ *!' t2' V t5, t8t Fr0m the T'graph it is Poaslble

to develop further indices which are useful for the comparative analysis of

tasks.

Consider the notion of inter-task co-ordination, that is, setting the

tasks in order so chat the goal might be reached. Intuitively, 11 appears that

a group task requires more co-ordination as the number of precedence relation-

ships between tasks increar^s. Consider a 4-person group with four tasks

such that each person has one task. The possible ways of ordering the tasks

are set out in Figure 12.

The digraphs set out in Figure 3 2 are Incomplete T-graphs because no

beginning tisk has been specified. For calculating an Inter-task co-ordination

index, these initial tasks will be left out. The graphs themselves resemble

the types of networks used for studies of communication, the inter-task-co-

ordlnatlon index can be expressed as the sum of the distances from one point to

all others, summed over all points. For instance, in graph 1, thf distances

from t to t2, t_, t. respectively are 1, 2, 3. The distances from t to t-,

t. are 1, 2 respectively. The C for graph 1 then is

(1 + 2 + 3) + (1 + 2) + (1) + (C) « 10.

(1) (2)

> t > t > 2 3

4

Figure 12.

Incomplete T-graph of possible precedence orderlngs t' 'our tasks

(Continued on page 33)

33.

(3) (4)

Figure 12.

Incomplete T-graph of possible precedence orderlngs of four tasks

C for Figure 12 examples (2), (3) and (4) are 8, 7, and 3 respectively.

These figures are taken to "vcan that the distribution of tasks as In (1)

demands more inter-task co-ordination than for (4), while (2) and (3) make

intermediate demands.

Formally, then, the C index is constructed by (a) forming the digraph

D consisting of all task.* except the beginning task; (b) calculating the C tt

index value from I « 1

C a £ a tt 1

1-1

where n « number of tasks in the sub-set of tasks vhich excludes the Initial

task, a = the distance sum from task t and Is equal to the sum of the

finite distances (t., t ), for all 1, n. l n

Another property of the T-graph depicted in Figure 12 is the number of

alternative paths from the beginning to the end. It would be desirable to

have some method of finding the number r! alternate paths In a group task

(cf. goal path multiplicity, Shaw (1963) ), It appears possible to use some

theorems of digraph theory developed by Harary, Norman, and Cartwright (1965).

The theorems are concerned with the number ox paths of given length in a digraph.

Consider digraph (2) In Figure 12. The points and lines cf this digraph can

be represented by an adjacency matrix (d) In which the rows and columns corres-

34.

pond to points of D and the entry a « 1 if line t t Is In D, while a = 0

if t t Is not in D. 1 J

A(D)

0 110

0 0 0 1

0 0 0 1

0 0 0 0

In order to calculate the number of point-line sequences In D of length

a, the nth power of the matrix is computed. In A(D) the 1, J entry Is the

number of sequences In D of length n from t to t , A point-line sequence Is

an alternating sequence of points ano. lines which begins and ends with a point

and has the property that each line is preceded by its first point and follow-

ed by its second point. There is no restriction on the number of times a point

or line may be repeated in the same sequence. Not all sequences are paths,

since it Is possible for the same point to be encountered more than once.

Let P be the matrix whose 1, J entry is the number of path;? of length

n from t to t . A sub-graph D is now specified which Is obtalred from A(D)

by replacing every entry in the j' row and * 1 column of A by 0. Let P (D.) n J

be the matrix of n-paths in D . According to Theorem 5.26 (Harary, Norman, &

Cartwright, 1965) the matrix P of n-paths of digraph D may be expressed in n

terms of the matrices of (n-1) paths of each of its sub-graphs D by specifying

its columns: the J column of P Is the same as the J column of the product n

P^JCDJ) • A(D) for j = 1, 2 p.

This theorem will be Illustrated using the digraph D with four points

shown In Figure 12(2).

35.

PjCD) «

W •

0 110

0 0 0 1

0 0 0 1

0 0 0 0

0 0 10

0 0 0 0

0 0 0 1

0 0 0 0

w

P1<D1> ■

0 110

0 0 0 0

0 0 0 0

0 0 0 0

^ N 0 0 0 0

0 0 0 1

0 0 0 1

0 0 0 0

s P1<D3) ^ 0 10 0

0 0 0 1

0 0 0 0

0 0 0 0

.th Calculating th© J column of the product PjCD,) * A(D) for J « 1 ....4

the matrix of two paths of D is found to be

P2(D) 0 0 0 2

0 0 0 0

0 0 0 0

0 0 0 0

This matrix indicates that there are only two paths of length 2 in D and

these are both from t to t , as can be verified by inspection in this simple

case.

The relation of the above procedure to the "Critical Path Method" (Shaffer,

et al., 1965) will be obvious.

Clearly, the specifications of the three indices for inter-position col-

laboration, Intcr-posltiou co-urdination, and nter-task co-ordination give

greater precision to the previously rather vague definitions of "co-operation"

and "task complexity" or "task difficulty." Further investigation of the

properties of the interaction between these indices is possible, but is beyocd

th«. scope of this report.

•• •

36.

Summary

A beginning has been made towards an analysis of group tasks. Structural

role concepts are used to relate the task system to other elements of a group,

and indices are derived to measure the amount of Inter-position collaboration,

intar-position co-ordination, and inter-task co-ordination demands. A way of

conceptualizing goal path multiplicity in terms of digraph theory is also given.

A general problem in need of Investigation is the manner in which a task

system may generate different sets of relationships in the P graph and the H

graph. One example is that when two positions have to collaborate in a task, a

communication relationship must be set up between these two positions in addition

to any power relationship already defined on them. These relatlonbliips in turn

will generate one or more informal relationships such as liking, deference or

admiration.

A practical problem associated with the application of this type of task

analysis concerns the identification of sub-tasks. In order to draw a digraph

representing an actual group task it is necessary, firstly, to identify the con-

stituent sub-tasks and secondly, to specify the precedence relationship ordering

these sub-tasks. In some groups, it is relatively easy to represent the group

tasks, e.g., for an assembly }ine in an automobile factory. Before the finished

product can be completed, there are a series of operations performed by men on

machines and materials. These operations are either capable of being identified

^ are explicit in the production plan. Furthermore, precedence relationships

are generally explicit or are obvious from the actual layout of the material

flow system.

For other tasks, the sub-tasks and precedence relationships cannot be easily

inferred from observation of physical operations or material flow system. In

problem-solving tasks, the sub-tasks may be best inferred from er» analysis of

i I^M ■- ■ ■ ■ ■ . -, -^-.-^ t ,-, r . .=.-.-. ..- .--.--■ - _^ .--,=-.-. ^-,-^- ^. -,- I ,.-.-..:-..- ..-. ,._. ^ ^,, -,.-■. ^.-.r-^.,-. ,1-.^-.^^-...J.i.. .-r- - .-^J-.—«» T*. j... -i-^.,-»-f rr-IM II ' li *■ *

37.

the problem Itself. Necessary steps In reasoning or calculating are generally

Identifiable.

In some tasks, however, neither physical aor logical operations may be

used as a basis ofr drawing the T graph. Theoretical analysis, rather than

"empirical" or "logical" analysis must be used. An example is a creative task.

When a novel product is required, then there are no routine physical or logical

sub-tasks. If a T graph is to be drawn, then it must be done with a particular

theory of the creative process. Thus, the procedures for applying this task

analysis may vary according to the type of task. A further difficulty Is the

level of analysis to be used. For a discussion task, should it be represented

as one task, "discussion," or a number of sub-tasks be.g., opinion-expressing,

opinion-evaluating, etc.)? What level of analysis Is used depends partly on

the theoretical problem being Investigated. So, generally, the interpretation

(or operational definition) given to "sub-task" depends a the type of task,

the purpose of the investigation, and the careful ingenuity of the Investigator.

It is Important to note however, that this problem of the level of analysis

is not a difficulty unique to the structural role thoery approach to task des-

cription. Indeed, the problem is general whereover operational definition is

used in the absence of established conventions for measurement. Within this

limitation, it appears that the method of task analysis described in this report

represents a substantial advance in that it

(a) deals with a comprehensive set of group elements and relationships

(b) provides a way of relating the task system to group structure end

process

(c) develops a set of Indices to describe some of the ways in which persona

and positions in a group may be related to the task structure.

These indices give precise quantification and may be used quite generally to

d crlbe the task structure of a wide range of groups.

i i

. - - ü—

38.

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DD form 1473

DOCUMENT CONTROL DATA - R&D

1. ORIGINATING ACTIVITY (Corporate author)

Group Effectiveness Research Laboratory Department of Psychology University of Illinois, Urbana, Illinois

2a.

3.

5.

6.

7a.

7b.

8a.

8b.

c. d.

9a.

10.

REPORT SECURITY CLASSIFICATION

Unclassified

REPORT TITLE

Methods of Analyzing Group Tasks

DESCRIPTIVE NOTES (Type of report and inclusive dates)

Technical Report.

AUTOOR(S)

Gordon O'Brien

REPORT DATE

January, 1967

TOTAL NO, OP PAGES

42

NO. OF REF.

52

CONTRACT OR GRANT NO,

Nonr 1834(36)

PROJECT NO.

2870 NR 177-472 ARPA Order #454

ORIGINATOR'S REPORT NUMBER

Technical Report No. 46

AVAILABILITY/LIMITATION NOTICES

DISTRIBUTION OF THIS DOCUMENT IS UNLIMITED

L.

DD for» 1473

12. SPONSORING MILITARY ACTIVITY

Department of the Navy Office of Naval Research Group Psychology Branch

13. ABSTRACT

In this report, It la argued that description and classification of group tasks can host be approached from a theoretical rather than empirical or factor analytic perspective. It is pointed out that previous attempts at task classification generally focus en one of three aspects of the task and group situation. The literature of group task analysis dealing with each of these aspects is then reviewed, and it is pointed out that each kind of task classification can be comprehended as an attempt to discriminate different relations existing between various elements of the task and group structure. The contribution of these attempts to a theoretically useful taxonomy of tasks Is evaluated.

Structural role theory is Introduced as a theoretical framework which loads to a system for classifying tasks. Digraph theory and matrix algebra are then applied to the problem of task definition, and indices for the measure- ment of some Important group task dimensions (inter-position collaboration, inter-position co-ordination, inter-task co-ordination, and goal path multipli- city) are derived. Ih* report concludes with a brief discussion of the problems and advantage? of application of the structural role theory method of task analysis.

14. KEY WORDS

Group tasks Structural role theory Co-operation Goal path multiplicity